Diffraction theory and visual hyperacuity

The implications of the diffraction theory of light are examined as they relate to visual acuity and hyperacuity. Two incoherent point sources of light give rise to a double-peaked light distribution whose trough is 26% below the adjoining peaks when the sources are separated by Rayleigh limit of resolution, but the dip has vanished when the separation is 80% of the Rayleigh limit. Diffraction theory, however, places no restriction on the precision with which any single source can be localized. No paradox is therefore involved in having a point-spread function with half-width one minute of arc and, at the same time, a localization threshold of a few seconds of arc, although the need for a sophisticated processing mechanism to achieve such low hyperacuity thresholds is emphasized.